An integrated macroelement formulation for the dynamic response of inelastic deformable rocking bodies

This paper presents a macroelement formulation for the prediction of the planar dynamic response of inelastic deformable rocking bodies. The formulation is based on a previous macroelement developed by the authors able to describe the cyclic response of inelastic rocking bodies, which takes into account the deformability both along the height of the member, as well as near the rocking end. Modifications of this formulation to account for other motion modes of rocking members during their dynamic response, namely, sliding and upthrow, as well as modifications to account for damping in a uniform manner during the whole motion, including impacts, are introduced. The dynamic response predicted by the macroelement for free-standing rigid and deformable rocking bodies is presented and compared with existing theoretical solutions, and the effect of deformability, damping, inelasticity, and friction on the response is discussed.